This article develops a one-sample test for H₀: F¯ = F¯₀ in presence of random right censoring. The test statistic is of particular interest when the alternative hypothesis is that the survival ratio ψ = F¯/F¯₀ is monotone. It is proved that the test statistic is asymptotically normal under H₀. The specific case where the censoring and survival times have proportional hazards is also considered. Finally, the testing procedure is applied to two well-known data sets.